The State of Missouri, facing a deadline today for changing the way it executes condemned prisoners by lethal injection, told a federal judge last night that it was simply unable to meet his demand that the state hire a board-certified anesthesiologist to oversee executions.

The judge, Fernando J. Gaitan Jr. of the United States District Court for the Western District of Missouri, had demanded an overhaul of the system after the doctor who now mixes the drugs for the state described an improvised process that Judge Gaitan found so chilling that he temporarily barred executions in Missouri.

A United States Supreme Court ruling last month made it easier for death row inmates to challenge procedures used in lethal injection, and legal cases across the country are questioning whether the methods cause unconstitutional pain and suffering.

With state officials’ response last night outlining changes to their procedures, Missouri has moved to the center of the charged debate over the technique, which is used in executions in 37 states.

In a sworn deposition, the Missouri doctor, whose name is being withheld by the state, acknowledged that he had sometimes given the condemned a smaller dose of anesthesia — used to reduce the pain of the lethal drugs to come — than the state had said was its policy.

The doctor said he was solely responsible for counting out dosage amounts of the three drugs administered in sequence, knew of no written protocol by the state for carrying out executions and was at times “improvising.”

He also said he is dyslexic, sometimes mixing up phone numbers or cable bill account numbers. “So it’s not unusual for me to make mistakes,” the doctor, identified in court records as John Doe I, said.

He indicated in his testimony, however, that he had made no mistakes in his death chamber work and that the mistakes elsewhere were “not medically crucial.”

Judge Gaitan said he was “gravely concerned” about the doctor’s dyslexia and criticized the lack of “checks and balances,” ruling on June 26 that the state was subjecting the condemned to “an unnecessary risk that they will be subject to unconstitutional pain and suffering when the lethal injection drugs are administered.”

The judge ordered Missouri to hire a board-certified anesthesiologist (John Doe I is a surgeon), and gave the state until today to submit a formal, written set of procedures, including increased monitoring of inmates and an assurance of sufficient anesthetic drugs.

But in the state’s filing last night, officials said they had sent letters to 298 certified anesthesiologists who reside anywhere near the state’s death chamber in Bonne Terre, and were turned down by all of them.

“A requirement of using a board-certified anesthesiologist is a requirement that cannot presently be met,” Attorney General Jeremiah W. Nixon wrote. “To enforce it may effectively bar implementation of the death penalty in Missouri. Surely that is not what the court intended.”

It was uncertain whether the judge, who could not be reached late last night, would accept the state’s alternative: Missouri officials said they would instead use “medical personnel in roles appropriate,” like a physician, nurse or pharmacist preparing the drugs.

It was unclear from the filing whether the state intended to retain John Doe I. The American Society of Anesthesiologists and the American Medical Association say physicians should not take part in executions, and Orin F. Guidry, the president of the A.S.A., recently issued a letter to members reiterating that position in light of the Missouri ruling.

It is increasing clear that people want the death penalty in abstract, not in practice. They like the idea of killing the heinous, but when it comes to actually doing so, they are far less eager to go about it. It is only a matter of time before we end it. It ended in New York with a wimper and isn't even an issue in statewide races. It was so cumbersome, no one used it. They tried and the disparites were too much to overcome. No death penalty in New York or Bronx Counties, but in Queens and Kings and Richmond.

Pataki tried to make some noise about it, but no one was that upset when it went away.